Question: Emily is 30 years older than Ashley. Eighteen years ago, Emily was 4 times as old as Ashley. How old is Emily now?
Answer: We can use the given information to write down two equations that describe the ages of Emily and Ashley. Let Emily's current age be $e$ and Ashley's current age be $a$ The information in the first sentence can be expressed in the following equation: $e = a + 30$ Eighteen years ago, Emily was $e - 18$ years old, and Ashley was $a - 18$ years old. The information in the second sentence can be expressed in the following equation: $e - 18 = 4(a - 18)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $e$ , it might be easiest to solve our first equation for $a$ and substitute it into our second equation. Solving our first equation for $a$ , we get: $a = e - 30$ . Substituting this into our second equation, we get the equation: $e - 18 = 4($ $(e - 30)$ $ -$ $ 18)$ which combines the information about $e$ from both of our original equations. Simplifying the right side of this equation, we get: $e - 18 = 4e - 192$ Solving for $e$ , we get: $3 e = 174$ $e = 58$.